Polyhedra

High School Math based on the topics required for the Regents Exam conducted by NYSED.

What is a Polyhedron?
A polyhedron is a 3-dimensional figure with faces made of polygons. More than one polyhedron is called polyhedra. The most common polyhedra are pyramids and prisms.
Other types of polyhedra are named by their orientation (right or oblique) and the shape of their bases (triangular, rectangular, hexagonal etc.).They can also be classified as concave or convex.

What are platonic solids?
Platonic solids are polyhedra that have all congruent faces, edges and vertex angles. There are only five platonic solids called tetrahedron, hexahedron (cube), octahedron, dodecagon, and icosahedron.

What is the Euler's Theorem?
The Euler's Theorem relates the number of faces, vertices and edges on a polyhedron.
F (Faces) + V (Vertices) = E (Edges) + 2

Polyhedrons: Lesson (Basic Geometry Concepts)
In thie lesson, you'll learn what a polyhedron is and the parts of a polyhedron. You'll then use these parts in a formula called Euler's Theorem.

Polyhedrons: Lesson (Geometry Concepts)
In this lesson, you'll learn how to identify polyhedron and regular polyhedron and the connections between the numbers of faces, edges, and vertices in polyhedron.

Polyhedrons: Lesson (Geometry Concepts)
This video shows how to work step-by-step through one or more of the examples in Polyhedrons.
1. Determine if the following solids are polyhedrons. If the solid is a polyhedron, name it and dertermine the number of faces, edges and vertices each has.
2. In a six-faced polyhedron, there are 10 edges. How many vertices does the polyhedron have?

Euler's Theorem
F + V - E = 2

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